Structural statistical properties of knotted proteins

The composition and residue–residue interactions of knotted proteins, compared with those of other proteins, can provide considerable insight into the driver of the knots in proteins. In this paper, we calculate the probabilities of 20 amino acids in 273 knotted entries from the Protein Data Bank (PDB). The collection of 273 entries contains all knotted structures in the PDB, and it is not a subset. With an appropriate value of R c , the numbers of all residue–residue contacts are counted in all 273 knotted structures. To make an accurate comparison, we count up to 9000 other entries from the PDB as well, and these entries spread over all sorts. In knotted structures, Leu occupies a maximal proportion of 9.62% among all 20 amino acids, and Leu, Phe, Trp, Gly, His, Gln, Asp, Lys and Pro may all play a more important role. Also, we analyse the effects of amino acid residues on the long-range contacts. We observe a larger average number of long-range contacts in the knotted structures than that in other ones, implying their important role in achieving the knots. Accordingly, the average number of short-range contacts becomes small when the structure becomes knotted because it depends mainly on the short-haul sequence of amino acids to form the short-range contact. In addition, the shape distribution of knotted proteins and the contrast with the other proteins are also presented. A comparison shows that the knots may make structures more globular because the average shape factor is 0.059 for the knotted proteins, which is only about 1/3 of the average shape factor for the other proteins.